![]() As previously mentioned, a cassette should be chosen for a specific riding style and locale-otherwise, we find little enjoyment trying to keep up while fighting our gears. Now onto the practical portion of gearing. ![]() The online calculators are much more practical, but sometimes an appreciation for the background calculations is a good thought to hang onto while pouring on the power mile after mile. Luckily, there are many useful gearing calculators online which a user can select gear combinations by number of teeth, input a cadence and wheel size, and find out speed. I’ve also found the following calculator to be useful-although seemingly daunting at first glance. In general, the gold standard for bicycle information is Sheldon Brown’s website which includes a gearing calculator. We know what the angular tooth spacing of a bicycle gear is, since chains are a standard size, but to calculate along this path much further would only serve to keep us at our desks calculating rather than actually riding. Unfortunately, this discussion has been more on the academic side, so a gearing ratio based on the radius of the gears is hardly practical when gears are measured in number of teeth. Knowing our desired cadence and gearing ratio, we can determine a speed. The image below shows everything discussed in the preceding paragraphs-it is messy, but it’s all there start at the crank and the beginning of the previous paragraph and work towards the wheel speed at the end of this paragraph. ![]() Since we calculate a linear velocity by multiplying the angular velocity and the distance from the axis of rotation, we can calculate the angular velocity of the cassette to be the angular velocity of the chainrings multiplied by the ratio of cassette cog radius to chainring radius.Ĭassette angular velocity? Since we don’t measure that with a cadence sensor, is it really that important? Well, we in fact do measure the angular velocity of the cassette, we just find it easier to measure it after it’s been multiplied by the radius of our rear tire-then we call it speed and occasionally measure it with GPS satellites 22,000 miles above the earth. The cassette sees a chain speed come from the chainring, and much like the chain rings, turns that linear velocity into a rotational velocity. Technically speaking, we do need to note that there is a chain speed to develop our gearing relationship, but nobody really cares at all except the cassette. ![]() So what, as long as the chain connects the chain rings to the cassette, why would we possiblly care about chain speed-I mean, have we ever seen that mentioned online or in magazines before?Ĭhain speed is absolutely meaningless. In the case of the chain, it is more useful to think of its linear velocity V in inches (or meters) per second. So we know we’re pedaling at ω and our gear teeth are rotating at ω as well is our chain also going at ω? Since we’re a little wild and crazy, assuming the chainrings do not deform while pedaling, let’s also assume the chain does not stretch significantly compared to its length while riding. The following image shows the fundamental relationship between angular velocity and tangential velocity. The magic happens where the radius at which this ω occurs, and we’ll see what that means in just a bit. Since we know the chainrings don’t deform while we pedal-no matter how strong we think we are, they don’t-we can assume that ω is the same at the crank spindle, at the chainring teeth, and at the pedal. (Radians are like degrees, a measure of angle.) Omega is the standard nomenclature for a rotational velocity with units of radians per second-measured about our crank spindle. Suppose we have a certain cadence, for convenience we’ll call it ω, the greek letter omega. Most people generally do not put a lot of thought into why this is the case, probably because knowing which gears go fast and which go slow is enough to make do. We all know that using different diameter gears can result in a very high speed or a very low speed for a given pedal speed. Follow the link below for our guide (or refresher!) to bike parts and anatomy: Before we get going, I want to make sure that we're all on the same page in terms of bike anatomy.
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